Nonlinear sliding mode observers for state and unknown input estimations

Sliding mode observers (SMO) for nonlinear uncertain systems are discussed from the perspective of the observability of unknown inputs. The unknown inputs are assumed to be bounded and not necessarily Lipschitz, and do not require any matching condition. A new nonlinear transformation is proposed and it divides the original system into two interconnected subsystems. The existence of sliding mode observers completely relies on the observability of unknown inputs w.r.t. output measurements. The robust terms or switching terms are designed such that the unknown inputs are tracked by their robust terms and so can be reconstructed from the sliding mode. The conditions for asymptotic stability of estimation error dynamics have been derived, based on Lipschitz assumptions for nonlinear functions, via standard Lyapunov analysis.

[1]  C. Kravaris,et al.  Geometric methods for nonlinear process control. 1. Background , 1990 .

[2]  Y. Soh,et al.  Robust observer with sliding mode estimation for nonlinear uncertain systems , 2007 .

[3]  Yi Xiong,et al.  Sliding mode observer for nonlinear uncertain systems , 2001, IEEE Trans. Autom. Control..

[4]  V. Utkin,et al.  Sliding mode observers. Tutorial , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[5]  J. Hedrick,et al.  Nonlinear Observers—A State-of-the-Art Survey , 1989 .

[6]  Chee Pin Tan,et al.  Sliding mode observers for fault detection and isolation , 2002 .

[7]  S. Żak,et al.  State observation of nonlinear uncertain dynamical systems , 1987 .

[8]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[9]  A. J. Koshkouei,et al.  Sliding mode state observation for non-linear systems , 2004 .

[10]  A. Isidori.  Nonlinear Control Systems , 1985 .

[11]  J. Barbot,et al.  Sliding mode observer for triangular input form , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[12]  J. Gauthier,et al.  Erratum Observability and Observers for Nonlinear Systems , 1995 .

[13]  Yeng Chai Soh,et al.  Robust discrete‐time nonlinear sliding mode state estimation of uncertain nonlinear systems , 2007 .

[14]  Y.C. Soh,et al.  Observer with multiple sliding modes for a class of nonlinear uncertain systems , 2005, Proceedings of the 2005, American Control Conference, 2005..